On the heels of the second alleged airstrike hitting a United Nations-run school in Gaza, with deadly effect, Israel declared a unilateral cease-fire on Monday morning, but cautioned that ongoing operations would continue, and any incoming fire would draw a response.

CBS News' Charlie D'Agata saw Israeli tanks rumble across dusty farmland near the Gaza border, apparently on their way out, but underground, the operation continued full-force.

Fifty feet below the tanks and a field of potatoes, Israeli forces discovered a tunnel cutting a direct course to a nearby kibbutz. It's more than two miles long, stretching from Gaza almost a mile into Israel.

Steel reinforced concrete, three feet wide, not quite six feet high, the tunnel is easily capable of accommodating a well-armed fighter.

Israeli Army Captain Daniel Elbo gave D'Agata a tour of what his government calls the "terror tunnels," and he said the militants thought of everything.

"Here you can see that there are cables," he told CBS News. "It is both electricity cables and phone cables." Elbo explained that because the tunnel is some 50 feet deep, cell phones don't work.

Israeli military officials say Hamas planned to use the dozens of tunnels penetrating Israeli territory to launch simultaneous attacks on soldiers and civilians. That made decimating the underground network the priority for ground forces in Gaza.

Israeli military officials say they've identified about three dozen tunnels like the one CBS News viewed, and that their destruction is just about complete.

But Israel's military admits, despite their best efforts, there are probably more tunnels they haven't picked up on yet.